**Casio fx-CG50 and Swiss Micros DM32: HP 16C’s Bit Summation**

**The
HP 16C’s #B Function**

The #B function is the HP 16C’s number of bits function and sums the bits that are “turned on”. To find #B, if needed, convert the number to its binary form (base 2). #B are the number of ones. Here, I am assuming the binary integers are unsigned.

For example: Calculate #B(49). Assuming 49 is in decimal base.

49_10 = 110001_2

Then #B(49) = 3

**Casio
fx-CG 50 Program: BITS**

I thought the fx-CG 50 had functions to convert integers and logical functions, but I did not have find them. If anyone knows whether the fx-CG 50 has base conversions, please let me know. I know that earlier Casio graphing calculators had base conversions.

The binary integer form is stored in B, as long as the decimal integer is less than 2048. (2^11).

Size: 168 bytes

“DEC→BIN”

“D”? → N

N → M

0 → C

0 → B

Int (log N ÷ log 2) → L

For L → J To 0 Step -1

If M ≥ 2^J

Then

C + 1 → C

M – 2^J → M

B × 10 + 1 → B

Else

B × 10 → B

IfEnd

Next

ClrText

If N < 2049

Then

“BIN=”

B ◢

IfEnd

“#B=”

C

The hashtag character (#) is called from the CHAR menu.

**Swiss
Micros DM32 Program: BITS**

Two labels are used:

LBL B: 68 bytes

LBL T: 92 bytes

The main program is LBL B. This should fit on the classic HP 32S/32SII calculators.

B01 LBL B

B02 CF 0

B03 SF 10

B04 “DEC NUMB”

B05 PSE

B06 INPUT N

B07 STO M

B08 Clx

B09 STO C

B10 RCL N

B11 LOG

B12 2

B13 LOG

B14 ÷

B15 IP

B16 1

B17 +

B18 STO L

T01 LBL T

T02 RCL M

T03 2

T04 RCL L

T05 1

T06 -

T07 y^x

T08 -

T09 x≥0?

T10 SF 0

T11 FS? 0

T12 LASTx

T13 FS? 0

T14 STO- M

T15 FS? 0

T16 1

T17 FS? 0

T18 STO+ C

T19 CF 0

T20 DSE L

T21 GTO T

T22 RCL N

T23 BIN

T24 STOP

T25 “BITS=”

T26 PSE

T27 CF 10

T28 DEC

T29 VIEW C

T30 GTO B

**Examples**

Decimal: 35, Binary: 100011, #B(35) = 3

Decimal: 36, Binary: 100100, #B(36) = 2

Decimal: 37, Binary: 100101, #B(37) = 3

Decimal: 50, Binary: 110010, #B(50) = 3

Decimal: 51, Binary: 110011, #B(51) = 4

Decimal: 52, Binary: 110100, #B(52) = 3

**Sources**

Hewlett-Packard.
__HP-16C Computer Scientists Owner’s Handbook__.
Hewlett-Packard Company. 1982. pg. 52

Eddie

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